Care tutte, cari tutti,

per il prossimo evento del ciclo dei Seminari di Analisi, giovedì 27 febbraio alle 17 in Aula Magna, avremo il piacere di ascoltare Giorgio Tortone (Università di Pisa), che terrà un seminario dal titolo "Some remarks on singular capillary cones with free boundary". Trovate l'abstract qui sotto.

Vi ricordiamo inoltre il seminario di oggi pomeriggio alle 17 in Aula Magna di Raoní Cabral Ponciano (UFABC, Brazil).

A presto,
Ilaria Lucardesi e Luigi Forcella

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Dear all,
on Thursday February 27th at 5PM in Aula Magna, for the Mathematical Analysis Seminar, we will have the pleasure of listening to Giorgio Tortone (Università di Pisa). The title of the talk is "Some remarks on singular capillary cones with free boundary". Please find the abstract below.

We remind you of the seminar of today at 5PM in Aula Magna by Raoní Cabral Ponciano (UFABC, Brazil).
See you soon,
Ilaria Lucardesi and Luigi Forcella

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Speaker: Giorgio Tortone (Università di Pisa)

Title: Some remarks on singular capillary cones with free boundary

Abstract: We discuss the existence of minimizing singular cones with free boundary associated to the capillarity problem. 
Precisely, we provide a stability criterion à la Jerison-Savin for capillary hypersurfaces and show that, in dimensions up to 4, minimizing cones with non-sign-changing mean curvature are flat. 
We apply this criterion to minimizing capillary drops and, additionally, establish the instability of non-trivial axially symmetric cones in dimensions up to 6. The main results are based on a Simons-type inequality for a class of convex, homogeneous, symmetric functions of the principal curvatures, combined with a boundary condition specific to the capillary setting.
This is based on a joint work with A. Pacati (ETHz) and B. Velichkov (UniPi).